In recent years, the study of the interplay between (fully) non-linear
potential theory and geometry received important new impulse. The purpose of
this work is to move a step further in this direction by investigating
appropriate versions of parabolicity and maximum principles at infinity for
large classes of non-linear (sub)equations F on manifolds. The main goal is
to show a unifying duality between such properties and the existence of
suitable F-subharmonic exhaustions, called Khas'minskii potentials, which is
new even for most of the "standard" operators arising from geometry, and
improves on partial results in the literature. Applications include new
characterizations of the classical maximum principles at infinity (Ekeland,
Omori-Yau and their weak versions by Pigola-Rigoli-Setti) and of conservation
properties for stochastic processes (martingale completeness). Applications to
the theory of submanifolds and Riemannian submersions are also discussed.Comment: 67 pages. Final versio
